diff options
Diffstat (limited to 'src/math/lgammaf_r.c')
| -rw-r--r-- | src/math/lgammaf_r.c | 250 |
1 files changed, 250 insertions, 0 deletions
diff --git a/src/math/lgammaf_r.c b/src/math/lgammaf_r.c new file mode 100644 index 00000000..9955b2f9 --- /dev/null +++ b/src/math/lgammaf_r.c @@ -0,0 +1,250 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.c */ +/* + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "libm.h" + +static const float +two23= 8.3886080000e+06, /* 0x4b000000 */ +half= 5.0000000000e-01, /* 0x3f000000 */ +one = 1.0000000000e+00, /* 0x3f800000 */ +pi = 3.1415927410e+00, /* 0x40490fdb */ +a0 = 7.7215664089e-02, /* 0x3d9e233f */ +a1 = 3.2246702909e-01, /* 0x3ea51a66 */ +a2 = 6.7352302372e-02, /* 0x3d89f001 */ +a3 = 2.0580807701e-02, /* 0x3ca89915 */ +a4 = 7.3855509982e-03, /* 0x3bf2027e */ +a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ +a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ +a7 = 5.1006977446e-04, /* 0x3a05b634 */ +a8 = 2.2086278477e-04, /* 0x39679767 */ +a9 = 1.0801156895e-04, /* 0x38e28445 */ +a10 = 2.5214456400e-05, /* 0x37d383a2 */ +a11 = 4.4864096708e-05, /* 0x383c2c75 */ +tc = 1.4616321325e+00, /* 0x3fbb16c3 */ +tf = -1.2148628384e-01, /* 0xbdf8cdcd */ +/* tt = -(tail of tf) */ +tt = 6.6971006518e-09, /* 0x31e61c52 */ +t0 = 4.8383611441e-01, /* 0x3ef7b95e */ +t1 = -1.4758771658e-01, /* 0xbe17213c */ +t2 = 6.4624942839e-02, /* 0x3d845a15 */ +t3 = -3.2788541168e-02, /* 0xbd064d47 */ +t4 = 1.7970675603e-02, /* 0x3c93373d */ +t5 = -1.0314224288e-02, /* 0xbc28fcfe */ +t6 = 6.1005386524e-03, /* 0x3bc7e707 */ +t7 = -3.6845202558e-03, /* 0xbb7177fe */ +t8 = 2.2596477065e-03, /* 0x3b141699 */ +t9 = -1.4034647029e-03, /* 0xbab7f476 */ +t10 = 8.8108185446e-04, /* 0x3a66f867 */ +t11 = -5.3859531181e-04, /* 0xba0d3085 */ +t12 = 3.1563205994e-04, /* 0x39a57b6b */ +t13 = -3.1275415677e-04, /* 0xb9a3f927 */ +t14 = 3.3552918467e-04, /* 0x39afe9f7 */ +u0 = -7.7215664089e-02, /* 0xbd9e233f */ +u1 = 6.3282704353e-01, /* 0x3f2200f4 */ +u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ +u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ +u4 = 2.2896373272e-01, /* 0x3e6a7578 */ +u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ +v1 = 2.4559779167e+00, /* 0x401d2ebe */ +v2 = 2.1284897327e+00, /* 0x4008392d */ +v3 = 7.6928514242e-01, /* 0x3f44efdf */ +v4 = 1.0422264785e-01, /* 0x3dd572af */ +v5 = 3.2170924824e-03, /* 0x3b52d5db */ +s0 = -7.7215664089e-02, /* 0xbd9e233f */ +s1 = 2.1498242021e-01, /* 0x3e5c245a */ +s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ +s3 = 1.4635047317e-01, /* 0x3e15dce6 */ +s4 = 2.6642270386e-02, /* 0x3cda40e4 */ +s5 = 1.8402845599e-03, /* 0x3af135b4 */ +s6 = 3.1947532989e-05, /* 0x3805ff67 */ +r1 = 1.3920053244e+00, /* 0x3fb22d3b */ +r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ +r3 = 1.7193385959e-01, /* 0x3e300f6e */ +r4 = 1.8645919859e-02, /* 0x3c98bf54 */ +r5 = 7.7794247773e-04, /* 0x3a4beed6 */ +r6 = 7.3266842264e-06, /* 0x36f5d7bd */ +w0 = 4.1893854737e-01, /* 0x3ed67f1d */ +w1 = 8.3333335817e-02, /* 0x3daaaaab */ +w2 = -2.7777778450e-03, /* 0xbb360b61 */ +w3 = 7.9365057172e-04, /* 0x3a500cfd */ +w4 = -5.9518753551e-04, /* 0xba1c065c */ +w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ +w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ + +static const float zero = 0.0000000000e+00; + +static float sin_pif(float x) +{ + float y,z; + int n,ix; + + GET_FLOAT_WORD(ix, x); + ix &= 0x7fffffff; + + if(ix < 0x3e800000) + return __sindf(pi*x); + + y = -x; /* negative x is assumed */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = floorf(y); + if (z != y) { /* inexact anyway */ + y *= (float)0.5; + y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ + n = (int) (y*(float)4.0); + } else { + if (ix >= 0x4b800000) { + y = zero; /* y must be even */ + n = 0; + } else { + if (ix < 0x4b000000) + z = y + two23; /* exact */ + GET_FLOAT_WORD(n, z); + n &= 1; + y = n; + n <<= 2; + } + } + switch (n) { + case 0: y = __sindf(pi*y); break; + case 1: + case 2: y = __cosdf(pi*((float)0.5-y)); break; + case 3: + case 4: y = __sindf(pi*(one-y)); break; + case 5: + case 6: y = -__cosdf(pi*(y-(float)1.5)); break; + default: y = __sindf(pi*(y-(float)2.0)); break; + } + return -y; +} + + +float lgammaf_r(float x, int *signgamp) +{ + float t,y,z,nadj,p,p1,p2,p3,q,r,w; + int32_t hx; + int i,ix; + + GET_FLOAT_WORD(hx, x); + + /* purge off +-inf, NaN, +-0, tiny and negative arguments */ + *signgamp = 1; + ix = hx & 0x7fffffff; + if (ix >= 0x7f800000) + return x*x; + if (ix == 0) + return one/zero; + if (ix < 0x35000000) { /* |x| < 2**-21, return -log(|x|) */ + if (hx < 0) { + *signgamp = -1; + return -logf(-x); + } + return -logf(x); + } + if (hx < 0) { + if (ix >= 0x4b000000) /* |x| >= 2**23, must be -integer */ + return one/zero; + t = sin_pif(x); + if (t == zero) /* -integer */ + return one/zero; + nadj = logf(pi/fabsf(t*x)); + if (t < zero) + *signgamp = -1; + x = -x; + } + + /* purge off 1 and 2 */ + if (ix == 0x3f800000 || ix == 0x40000000) + r = 0; + /* for x < 2.0 */ + else if (ix < 0x40000000) { + if (ix <= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ + r = -logf(x); + if (ix >= 0x3f3b4a20) { + y = one - x; + i = 0; + } else if (ix >= 0x3e6d3308) { + y = x - (tc-one); + i = 1; + } else { + y = x; + i = 2; + } + } else { + r = zero; + if (ix >= 0x3fdda618) { /* [1.7316,2] */ + y = (float)2.0 - x; + i = 0; + } else if (ix >= 0x3F9da620) { /* [1.23,1.73] */ + y = x - tc; + i = 1; + } else { + y = x - one; + i = 2; + } + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-(float)0.5*y); + break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); + break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-(float)0.5*y + p1/p2); + } + } else if (ix < 0x41000000) { /* x < 8.0 */ + i = (int)x; + y = x-(float)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch (i) { + case 7: z *= y + (float)6.0; /* FALLTHRU */ + case 6: z *= y + (float)5.0; /* FALLTHRU */ + case 5: z *= y + (float)4.0; /* FALLTHRU */ + case 4: z *= y + (float)3.0; /* FALLTHRU */ + case 3: z *= y + (float)2.0; /* FALLTHRU */ + r += logf(z); + break; + } + } else if (ix < 0x5c800000) { /* 8.0 <= x < 2**58 */ + t = logf(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else /* 2**58 <= x <= inf */ + r = x*(logf(x)-one); + if (hx < 0) + r = nadj - r; + return r; +} |